The two faces of capacitance: New interpretations for electrical impedance measurements of perovskite solar cells and their relation to hysteresis

Abstract

Perovskite solar cells are notorious for exhibiting transient behaviour not seen in conventional inorganic semiconductor devices. Significant inroads have been made into understanding this fact in terms of rapid ion migration, now a well-established property of the prototype photovoltaic perovskite MAPbI3 and strongly implicated in the newer mixed compositions. Here we study the manifestations of ion migration in frequency-domain small-signal measurements, focusing on the popular technique of Electrical Impedance Spectroscopy (EIS). We provide new interpretations for a variety of previously puzzling features, including giant photo-induced low-frequency capacitance and negative capacitance in a variety of forms. We show that these apparently strange measurements can be rationalized by the splitting of AC current into two components, one associated with charge-storage, and the other with the quasi-steady-state recombination current of electrons and holes. The latter contribution to the capacitance can take either a positive or a negative sign, and is potentially very large when slow, voltage-sensitive processes such as ion migration are at play. Using numerical drift-diffusion semiconductor models, we show that giant photo-induced capacitance, inductive loop features, and low-frequency negative capacitance all emerge naturally as consequences of ion migration via its coupling to quasi-steady-state electron and hole currents. In doing so, we unify the understanding of EIS measurements with the comparably well-developed theory of rate dependent current-voltage (I-V) measurements in perovskite cells. Comparing the two techniques, we argue that EIS is more suitable for quantifying I-V hysteresis than conventional methods based on I-V sweeps, and demonstrate this application on a variety of cell types.

Consistent Device Simulation Model Describing Perovskite Solar Cells in Steady-State, Transient, and Frequency Domain

“…With higher scan rate a pronounced hysteresis appears in the measurement and is well reproduced by the simulation. Here we confirm that even hysteresis-free devices can have a hysteresis that is shifted to different time scales, consistent with the finding of Jacobs et al 18 .…”

Influence of bromide content on iodide migration in inverted MAPb(I1−xBrx)3perovskite solar cells

“…Jacobs et al use a dri diffusion model to simulate the impedance response for PSC. 66 They show that 'giant photo induced capacitances', 'induction loops' and apparent 'negative capacitances' at low frequency can all be explained by the coupling of ion migration and electronic current. The only downside of models based on transistors and semi-conductor dri diffusion models is that complex numerical solutions are required to simulate the impedance response.…”

IonMonger: a free and fast planar perovskite solar cell simulator with coupled ion vacancy and charge carrier dynamics

“…Courtier et al [6] developed a finite element scheme, implemented in MATLAB [14], that is able to cope with the spatial and temporal stiffness of the problem and obtain accurate solutions to a coupled model for ion migration and charge carrier transport within the perovskite layer of a PSC. Since then, alternative numerical methods have also appeared in [13,27]. Walter et al [27] have developed a solver that includes the motion of both cations and anions.…”

“…While this provides a thoroughly tested and validated framework for their results, the model being solved only explicitly models the perovskite absorber and there is strong evidence suggesting that the adjacent transport layers play a key role in determining device behaviour [4]. Meanwhile, Jacobs et al [13] use the proprietary COMSOL package via a MATLAB interface to simulate three layers of a PSC over a range of timescales. However, the details of the modelling and solutions techniques are not given in full, making their results difficult to reproduce and compare with alternatives.…”